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Log-mean Linear Parameterization for Discrete Graphical Models of Marginal Independence and the Analysis of Dichotomizations

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  • Alberto Roverato

Abstract

type="main" xml:id="sjos12126-abs-0001"> We extend the log-mean linear parameterization for binary data to discrete variables with arbitrary number of levels and show that also in this case it can be used to parameterize bi-directed graph models. Furthermore, we show that the log-mean linear parameterization allows one to simultaneously represent marginal independencies among variables and marginal independencies that only appear when certain levels are collapsed into a single one. We illustrate the application of this property by means of an example based on genetic association studies involving single-nucleotide polymorphisms. More generally, this feature provides a natural way to reduce the parameter count, while preserving the independence structure, by means of substantive constraints that give additional insight into the association structure of the variables. © 2014 Board of the Foundation of the Scandinavian Journal of Statistics

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  • Alberto Roverato, 2015. "Log-mean Linear Parameterization for Discrete Graphical Models of Marginal Independence and the Analysis of Dichotomizations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 627-648, June.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:2:p:627-648
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    File URL: http://hdl.handle.net/10.1111/sjos.12126
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    References listed on IDEAS

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    1. Nanny Wermuth & Kayvan Sadeghi, 2012. "Sequences of regressions and their independences," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 215-252, June.
    2. Mathias Drton & Thomas S. Richardson, 2008. "Binary models for marginal independence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(2), pages 287-309, April.
    3. Robin J. Evans & Thomas S. Richardson, 2013. "Marginal log-linear parameters for graphical Markov models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 743-768, September.
    4. Nanny Wermuth & Kayvan Sadeghi, 2012. "Rejoinder on: Sequences of regressions and their independences," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 274-279, June.
    5. Thomas Richardson, 2003. "Markov Properties for Acyclic Directed Mixed Graphs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 145-157, March.
    6. Jokinen, Jukka, 2006. "Fast estimation algorithm for likelihood-based analysis of repeated categorical responses," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1509-1522, December.
    7. Anders Ekholm & John W. McDonald & Peter W. F. Smith, 2000. "Association Models for a Multivariate Binary Response," Biometrics, The International Biometric Society, vol. 56(3), pages 712-718, September.
    8. A. Roverato & M. Lupparelli & L. La Rocca, 2013. "Log-mean linear models for binary data," Biometrika, Biometrika Trust, vol. 100(2), pages 485-494.
    9. Monia Lupparelli & Giovanni M. Marchetti & Wicher P. Bergsma, 2009. "Parameterizations and Fitting of Bi‐directed Graph Models to Categorical Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 559-576, September.
    10. Tamás Rudas & Wicher P. Bergsma & Renáta Németh, 2010. "Marginal log-linear parameterization of conditional independence models," Biometrika, Biometrika Trust, vol. 97(4), pages 1006-1012.
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    1. Monia Lupparelli & Alberto Roverato, 2017. "Log-mean linear regression models for binary responses with an application to multimorbidity," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(2), pages 227-252, February.

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